I agree with the other authors in disgrediting your results. The bigger the crystallites are, the more the instrumental broadening must be taken into account. The best would be the fundamental parameters approach implemented in Topas, but only if the handling of this method is known.

But I disagree completely with the opinion the determination of crystallite size is limited to values below 100nm. Such a "limit" depends on the instrumental broadening of the instrument. Synchrotron radiation may provide extremly low instrumental broadening, standard lab goniometers may allow line widths below 0.05°, non focusing conditions will cause more significant broadening. With standard lab goniometer, correct instrumental broadening and taking the linear absorption coefficient into account you may distinguish between 300 and 400nm crystallite size (relative size). Absolute values may be determined upto a least 200nm. But this limit is not a fixed limit, because here "natura non facit saltus" is valid. results for bigger crystallite size are less reliable, less precise, but nut complete wrong when crossing the border. The reliability also depends on the material under investigation (triclinic?) and on the experience of the operator (preparation, measurement condition, evaluation method, general experience with microstructure) and on influences by other microstructural parameters (strain stacking faults, ...)

Please do not postulate a limit of 100nm without taking the other conditions into account.

Your question was: "Can the crystallite size only be determined when it is smaller than 100nm using XRD"

I believe the answer is yes, i.e., that XRD can only be used to determine crystallite size when the dimensions are less than ~ 100nm. This is because when the crystallites are larger than this, the peak broadening is really too small to measure.

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Your size calculation is wrong - you need to subtract the instrumental broadening from the measured peak breadth. Possibly TOPAS is doing this for you automatically, either using the correct instrumental parameters or is using some sort of default value (in which case the TOPAS answer is also wrong), whereas in EVA and in your hand calculation you have ignored the instrumental broadening and so the result is certainly wrong.

FYI - it is the "Scherrer" equation.

Try to record a spectrum using an internal standard (CeO2, for exapmle) with well-known (rather big) crystallite size. Then you will know the instrumental broadening

Respect to the limit of the size, I completely agree with Edward.

With respect to the way to calculate it with Topas, certainly you have to record a wide enough pattern from a line profile standard like LaB6 from NIST. The use it to calculate the instrumental contribution using in the fitting with Topas a TCHZ function but previously deactivating the Cry Size option, and the resulted parameters for the TCHZ have to be used in the real sample activating the option crystal size, and the value you get from LVol is the corrected one.

Using Topas and knowing the instrumental configuration if measuring in Bragg-Brentano geometry, the best option and easiest one is to use the Fundamental Parameters Approach. With this option you only need to use the FP peak type in the fitting process using the instrumental configuration used in the measurement. In this way you automatically will obtain the correct value in LVol without needed of use any standard.

I hope that will help you.

To prove the XRD calculation it is better to see SEM image. In this case you can avoid any problems with XRD uncerterness

Can we see grains with SEM if wafer surface is polished? Or Will we require EBSD?

As explained above: the result  is absolutely wrong, u have to extract the instrumental parameter from SRM and then use as the instrumental correction for the real specimen. Usually  SRM has crystallite size >1 um (refer to the SRM certificate for details).

 If u got ~160 nm with SRM, ur instrumental broadening is so big (~ 0.8 FWHM at 35.14 2theta ). Please re-check with Silicon SRM, att 2theta 47.285 or 56.105 to minimized axial divergence, the FWHM should be around 0.08 or smaller.

I agree with the other authors in disgrediting your results. The bigger the crystallites are, the more the instrumental broadening must be taken into account. The best would be the fundamental parameters approach implemented in Topas, but only if the handling of this method is known.

But I disagree completely with the opinion the determination of crystallite size is limited to values below 100nm. Such a "limit" depends on the instrumental broadening of the instrument. Synchrotron radiation may provide extremly low instrumental broadening, standard lab goniometers may allow line widths below 0.05°, non focusing conditions will cause more significant broadening. With standard lab goniometer, correct instrumental broadening and taking the linear absorption coefficient into account you may distinguish between 300 and 400nm crystallite size (relative size). Absolute values may be determined upto a least 200nm. But this limit is not a fixed limit, because here "natura non facit saltus" is valid. results for bigger crystallite size are less reliable, less precise, but nut complete wrong when crossing the border. The reliability also depends on the material under investigation (triclinic?) and on the experience of the operator (preparation, measurement condition, evaluation method, general experience with microstructure) and on influences by other microstructural parameters (strain stacking faults, ...)

Please do not postulate a limit of 100nm without taking the other conditions into account.

I do agree with Robert Haberkorn that with higher resolution instruments, the size limit can move up into the hundreds of nm range, but there are a lot of caveats. If the crystallite size has a fairly narrow gaussian distribution with equiaxed grains then the analysis can be pretty good. But that is very often not the case, and if not then your measurement will be biased by the large grains, and the crystallite size estimate will be fairly meaningless. I recall Prof Julia Weertman at Northwestern University making this point at a meeting some years ago - there may be some publications that describe it in more detail.

And on the same topic, think about the irradiated volume of material. If the volume is relatively small and the crystallite size is relatively large, then your diffraction peaks will become less statistically significant. You win some back if you use a large area 2D detector, as is common at synchrotron facilities, but it still approaches becoming a problem of knowing how representative of the bulk your data is. This is a common issue with electron microscopy also - you get a lot of detail about a very small region and try to extrapolate this across the entire sample.

XRD's average crystalline size will be somewhat accurate if it is lesser than 150nm.

1. There is nothing uncertain about XRD! "XRD uncertainty" is caused by the use of archaic detectors with "spatial blindness" and resorting to "groping in the dark" :-) Might as well go back to the film/potodensitometer combination of the Debye-Scherrer original method. Not to be confused with "Scherrer Equation" that Edward Andrew highlighted :-)

2. 0.8 degree  FWHM for the system is "gross". You folks are using this ultra sensitive tool as a "sledge hammer".

3. In my opinion, there should be no limits to the determination of size through periodicity that affect the reciprocal space profile. We are routinely determining strain field variations in the FEMTOMETER scale using the XRD rocking curve method. It is just a matter of optics used, SNR (signal to noise ratio) and the sensitivity of the 2D detector. Forget the paleolithic 0D point counter and the related conventional linear diffractogram. Unless you use the "whole pattern method" (Scardi, Leoni et.al.), you don't even stand a chance.

4. Conventional linear diffractograms do not provide the resolution in reciprocal space for unequivocal conclusions and interpretations. Every attempt I see at interpreting such diffractograms are rife with ambivalence.

5. In practice and real life, particles are not as one models them to be. So there is bound to be difference between computed and actual sizes. Add to it the complication created by preferred orientation, discrete size distribution, sample positioning, alignment, etc., you get a big fat unintelligible "MUSH" (convolution) that requires super special mathematical machinations to decipher.

6. XRD is the best NDE method to estimate "particle size". However, it must be calibrated with suplimentary tools like EBSD, SEM, TEM etc. Using "known standards" is the key!

BOTTOM-LINE: The XRD method you are using presently will at best only serve you as a relative measurement tool. But a darned good one! Just find yourself some good "well known standards" to compare with :-) 

https://www.flickr.com/photos/85210325@N04/10242907544/in/set-72157645018820696

I calculated av. crystallite size of my zeolite sample

Lambda is 10 nm

2theta is 29.3 degree

beta is 0.75 degree

Dp comes as -6.15 nm

What does minus value imply.Please help.

"Lambda is 10 nm" - What is the anode material?

What beam conditioner?

"beta is 0.75 degree" - Do mean FWHM? Do you know the relationship between beta & FWHM? This would depend on the shape of the Bragg profile. Do remember to convert to Radians for use.

What calibration standard did you use to estimate "instrumental broadening"?

"What does minus value imply." - Generally, lack of information :-) 

!0 nm is about 123 eV. So your entire diffractometer must be in a vacuum chamber! However, even in a vacuum chamber you aren't going to see diffraction at 29.3 degrees at that energy. Funny stuff.

T. S. Gokul Raja Please, can you recommend a reference on size ranges that can be reliable?